# Rasa Puzzle

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You are given a square board (4×4, 6×6 or 8×8) with numbers as tokens.

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You have to eliminate all tokens in as few moves as possible. A move consists of adding or subtracting two rows or two columns at a time.

If a token is the only one in its row and column, it disappears.

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Contributed by: Karl Scherer (April 2013)
Open content licensed under CC BY-NC-SA

## Details

The shortest solutions (for setups 1, 2, and 3 of boards 4x4 and 6x6) have been found by the author by hand, so you may be able to improve on them.

The best solutions for the three 8x8 setups are not known.

You can also create your own setup.

Move description

Select a row or column by clicking one of the arrows.

Then select a second row (or a second column) by clicking one of the plus signs or minus signs that appear instead of the arrows.

If you click a plus sign, the second selected row (or column) will be added to (or subtracted from) the first selected row or column.

If an token is zero, it will not be displayed.

The goal is to reduce the sum of the absolute values of the tokens as much as possible.

This sum is displayed at the left border.

Controls

"board size": select the size of the board (4x4, 6x6 or 8x8).

"setup": there are three challenges with fixed setups for each board size. The fourth setup has an empty board. Click one of the corner positions of the empty fourth board to randomize the setup, or click board positions repeatedly to manually set up the board. Once you start moves you cannot change the setup anymore.

"colored": here you select whether you want the tokens colored or white only.

"moves done": displays the number of the current move and also the total amount of moves.

"<<, < 10, <" and ">,> 10, >>": these two setter bars let you select previous moves etc.

"repeat move 1x / 10x": click to repeat the last move once or ten times. These options are not available after a "lonely" token (one that is the only occupant of its column and row) has been deleted. Also, only some of the "10x" ten times repeat moves will be executed if a "loner" is eliminated during this automatic play. This does not create any problems. Just be aware that not all 10 moves might be executed in such a case (you will see that the move counter is not increased by 10 in these cases).

"save/restore": saves and restores the current sequence of moves.

"token count": this is the sum of the absolute (positive) values of all tokens on the board. Try to make this sum as small as possible.

"target": this is the smallest token count the author has found. Can you get this count or even improve on it?

"solution": solutions are stored only for the setups 1 to 3 which use the board 4x4 and 6x6. Use the paging control ("<<","<",">",">>") to go through a solution move by move.

History

The Rasa puzzle got its name from the Latin expression "tabula rasa" (clean slate), because it ends with an empty playing board.

## Permanent Citation

Karl Scherer "Rasa Puzzle"
http://demonstrations.wolfram.com/RasaPuzzle/
Wolfram Demonstrations Project
Published: April 22 2013

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